Title: Results on Lorentzian metric spaces Show Chinese title

Title: 关于洛伦兹度量空间的结果

Abstract: We provide a short introduction to ``Lorentzian metric spaces" i.e., spacetimes defined solely in terms of the two-point Lorentzian distance. As noted in previous work, this structure is essentially unique if minimal conditions are imposed, such as the continuity of the Lorentzian distance and the relative compactness of chronological diamonds. The latter condition is natural for interpreting these spaces as low-regularity versions of globally hyperbolic spacetimes. Confirming this interpretation, we prove that every Lorentzian metric space admits a Cauchy time function. The proof is constructive for this general setting and it provides a novel argument that is interesting already for smooth spacetimes. Show Chinese abstract

Abstract: 我们提供对“洛伦兹度量空间”的简短介绍，即仅通过两点洛伦兹距离定义的时空。 如先前工作所述，如果施加最小条件，例如洛伦兹距离的连续性和时间类钻石的相对紧性，这种结构基本上是唯一的。 后一个条件对于将这些空间解释为全局双曲时空的低正则性版本是自然的。 证实这一解释，我们证明每个洛伦兹度量空间都包含一个柯西时间函数。 该证明在这一一般设置中是构造性的，并提供了一个新颖的论证，即使对于光滑时空也具有重要意义。